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Example 1
1. A large plane sheet has an area of 50 cm2 and has a charge of 3mC uniformly distributed over it. Find the Surface Charge Density.
Solution:
q = 3 mC = 3 × 10–3 C, A = 50 cm2 = 5 ×10–3 m2, σ = ?
σ=qA=(3×10−3)(5×10−3) = 0.6Cm−2
2. A cuboidal box penetrates a huge plane sheet of charge with uniform Surface Charge Density 2.5×10–2 Cm–2 such that its smallest surfaces are parallel to the sheet of charge. If the dimensions of the box are 10 cm × 5 cm × 3 cm, then find the charge enclosed by the box.
Solution:
Charge enclosed by the box = charge on the portion of the sheet enclosed by the box.
The area of the sheet enclosed; A = area of the smallest surface of the box
= 5 cm × 3 cm = 15 cm2 = 15 × 10–4 m2
Charge density; σ= 2.5 ×10–2 Cm–2
Charge enclosed; q = σA = (2.5×10−2)(15×10−4) = 37.5×10−6C = 37.5µC
Practice question:
The same charge is given to four thin plane laminas of different shapes; an equilateral triangle, a square, a regular hexagon, and a circular one. All of these have the same perimeter. Then the lamina with the maximum Surface Charge Density has the shape as that of :
- an equilateral triangle
- a square
- a regular hexagon
- a circle
Ans (a)
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